Monitor position determining apparatus and monitor position determining method

ABSTRACT

A monitor position determining apparatus includes an acquiring unit that acquires design data concerning circuit elements arranged in a layout of a semiconductor device and for each of the circuit elements, yield sensitivity data indicative of a percentage of change with respect to a yield ratio of the semiconductor device; a selecting unit that selects, based on the yield sensitivity data, a circuit element from a circuit element group arranged in the layout; a determining unit that determines an arrangement position in the layout to be an installation position of a monitor that measures a physical amount in the semiconductor device in a measurement region, the arrangement position being of the circuit element that is specified from the design data acquired by the acquiring unit and selected by the selecting unit; and an output unit that outputs the installation position determined by the determining unit.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority of theprior Japanese Patent Application No. 2008-186162, filed on Jul. 17,2008, the entire contents of which are incorporated herein by reference.

FIELD

The embodiments discussed herein are related to a technology that, basedon feedback process control, improves the fabrication yield of asemiconductor device formed on a semiconductor wafer.

BACKGROUND

In recent years, with the miniaturization of technology, the influenceof statistical factors, such as process variation becomes significant,increasing circuit delay, leak fluctuations, etc. Circuit delay and leakfluctuations are factors that reduce the yield ratio of a chip, andhence there is demand for a technology that controls process variationto improve yield ratio.

Conventionally, advance process control (APC), a technology that reducesvariation, has been disclosed as a technology that controls variationduring chip fabrication. APC is a technology that measures a physicalamount (e.g., a gate length or a film thickness) of a semiconductorwafer during fabrication and feeds back a result of the measurement tocontrol the physical amount (see, for example, Tsuchiya, Ryota; Izawa,Masaru; and Kimura, Shinichiro, “Prospect of Si Semiconductor Devicesand Manufacturing Technologies in Nanometer era”, Hitachi Hyoron, 2006,Vol. 88, No. 3, Line 20 in the right column on p. 44 (4.3 Problem andProspect of Mass Production Techniques) to Line 20 in the left column onp. 45, FIG. 10)

However, according to the conventional technology, a monitor thatmeasures a physical amount of a semiconductor wafer is arranged at aposition that is critical in terms of process (e.g., a position with areduced film thickness), while a critical position that is dependent oncircuit characteristics, layout, etc. is disregarded; hence, a problemarises in that this technology cannot cope with a reduction in yieldratio due to circuit dependent factors of variation.

SUMMARY

According to an aspect of an embodiment, a monitor position determiningapparatus includes an acquiring unit that acquires design dataconcerning circuit elements arranged in a layout of a semiconductordevice and for each of the circuit elements, yield sensitivity dataindicative of a percentage of change with respect to a yield ratio ofthe semiconductor device; a selecting unit that selects, based on theyield sensitivity data, a circuit element from a circuit element grouparranged in the layout; a determining unit that determines anarrangement position in the layout to be an installation position of amonitor that measures a physical amount in the semiconductor device in ameasurement region, the arrangement position being of the circuitelement that is specified from the design data acquired by the acquiringunit and selected by the selecting unit; and an output unit that outputsthe installation position determined by the determining unit.

The object and advantages of the invention will be realized and attainedby means of the elements and combinations particularly pointed out inthe claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and arenot restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic for explaining an overview of an embodiment;

FIG. 2 is a schematic of an overview of a monitor position determiningtechnique according to a first embodiment;

FIG. 3 is a block diagram of a monitor position determining apparatus;

FIG. 4 is a schematic of contents recorded in a parameter/yieldsensitivity table;

FIG. 5 is a functional diagram of the monitor position determiningapparatus according to the first embodiment;

FIG. 6 is a schematic of contents recorded in a similar-vector-distancetable;

FIG. 7 is a schematic of an exemplary monitor position table;

FIG. 8 is a schematic of an exemplary original point table;

FIG. 9 is schematic of another exemplary monitor position table;

FIGS. 10 and 11 are flowcharts of an example of processing fordetermining monitor position;

FIG. 12 is a schematic of an overview of the monitor positiondetermining technique according to the second embodiment;

FIG. 13 is a functional diagram of the monitor position determiningapparatus according to a second embodiment; and

FIGS. 14 and 15 are flowcharts of an example of processing fordetermining monitor position.

DESCRIPTION OF EMBODIMENT(S)

Preferred embodiments of the present invention will be explained withreference to the accompanying drawings. According to the monitorposition determining apparatus and the monitor position determiningmethod, parameter information that is a variation factor concerningyield sensitivity and layout with respect to circuit delay, a leakfluctuation, etc. of a semiconductor device at a design stage is used todetermine an installation position of an APC monitor, thereby improvingfabrication yield of the semiconductor device.

FIG. 1 is a schematic for explaining an overview of an embodiment. FIG.1 depicts an overview of a feedback type process control technology(APC) in an edging process of semiconductor device fabrication.

The APC is a technology that measures a physical amount (e.g., a gatelength, a film thickness, etc.) at a specific position of asemiconductor wafer during fabrication by using a monitor (a scanningelectron microscope) and feeds back a result of this measurement to anedging control device to control such a physical amount.

With respect to this technology, a position in a semiconductor waferwhere a physical amount is to be measured with a limited number ofmonitors is important. Conventionally, a monitor of the APC is set at aposition that is critical in terms of process, e.g., at an edge of asemiconductor wafer where film thickness is reduced. Here, a position atthe edge of the semiconductor wafer where the monitor is set isdetermined at random or at the discretion of the designer. However, thismethod cannot take a circuit-dependent factor of variation intoconsideration and cannot cope with a reduction in yield ratio due tothis factor in some cases.

Thus, according to the present embodiment, a position that isyield-critical in terms of circuit is specified based on circuitdependence information obtained at a design stage, and a monitor isprovided at this position. Specifically, a circuit element having a highyield sensitivity is specified from among a circuit element group in asemiconductor device formed on a semiconductor wafer, and an arrangementposition of this circuit element is determined as a monitor installationposition.

Here, similarities between variations of circuit elements are judgedusing parameters serving as variation factors concerning layout, and asfar as possible, each position having a different variation isdetermined as a monitor installation position. As a result, circuitdependent variations at a design stage can be efficiently andeffectively controlled with the limited number of monitors, therebyimproving process yield of a semiconductor device.

According to a first embodiment, for each element circuit of thesemiconductor device, parameters that are circuit dependent variationfactors are arranged in a vector space to obtain a multidimensionalvector. Parameters that are variation factors include, for example, anarrangement position, a gate length, and a gate width of a circuitelement in a layout of a semiconductor device.

Yield sensitivity indicative of a percentage of change in each circuitelement with respect to a yield ratio of a semiconductor device in termsof circuit delay, leak fluctuation, etc. is used to perform weighting.The yield sensitivity of each circuit element can be obtained by using acomputational expression acquired by a statistical analysis technique.In the present example, a higher yield sensitivity represents a circuitelement that is critical with respect to a yield ratio of thesemiconductor device.

FIG. 2 is a schematic of an overview of a monitor position determiningtechnique according to the first embodiment. As depicted in FIG. 2,vectors V1 to V3 of circuit elements P1 to P3 are depicted in a vectorspace 200 using three axes as parameters (an X coordinate of anarrangement position, a Y coordinate of the arrangement position, and agate length) that become variation factors of the circuit elements P1 toP3 in a semiconductor device.

Here, yield sensitivities of the circuit elements P1 to P3 aredetermined as “S1 to S3”, and a magnitude relationship between thesesensitivities is determined as “S1>S2>S3”. In this case, the circuitelement P1 having the greatest yield sensitivity S1 is selected, and anarrangement position (X1, Y1) of this circuit element P1 is determinedas a monitor installation position. Subsequently, the circuit element P2having the second greatest yield sensitivity S2 is selected, and avector distance between the vector V2 of the circuit element P2 and thevector V1 of the circuit element P1 already determined as the monitorinstallation position is obtained.

Here, when the vector distance between the vector V1 and the vector V2is larger than a preset similar-vector-distance, an arrangement position(X2, Y2) of the circuit element P2 is determined as a monitorinstallation position. On the other hand, when the vector distancebetween the vector V1 and the vector V2 is less than thesimilar-vector-distance, variations are considered to be similar, andthe arrangement position (X2, Y2) of the circuit element P2 is excludedfrom being a monitor installation position.

Since the vector distance between the vector V1 and the vector V2 islarger than the similar-vector-distance in this example, the arrangementposition (X2, Y2) of the circuit element P2 is determined as a monitorinstallation position. Then, the circuit element P3 having the leastyield sensitivity S3 is selected, and vector distances between thevector V3 of the circuit element P3 and the vectors V1 and V2 of thecircuit elements P1 and P2 already determined as the monitorinstallation positions are obtained.

Since a vector distance between the vector V3 and the vector V1 is lessthan the similar-vector-distance, an arrangement position (X3, Y3) ofthe circuit element P3 is excluded from being a monitor installationposition. This position is excluded to efficiently measure positionshaving different variations by the limited number of monitors andmeanwhile, control many variations.

As explained above, according to the first embodiment, tradeoff betweenmany parameters, e.g., yield sensitivities and similarities betweenvariation factors of the respective circuit elements in thesemiconductor device formed on a semiconductor wafer with respect to ayield ratio are adjusted to determine the installation position of eachmonitor. As a result, circuit dependent variations at a design stage canbe controlled, thereby improving the yield ratio of the semiconductordevice.

FIG. 3 is a block diagram of a monitor position determining apparatus.As depicted in FIG. 3, a monitor position determining apparatus 320includes a central processing unit (CPU) 301, a read-only memory (ROM)302, a random access memory (RAM) 303, a magnetic disk drive 304, amagnetic disk 305, an optical disk drive 306, an optical disk 307, adisplay 308, a interface (I/F) 309, a keyboard 310, a mouse 311, ascanner 312, and a printer 313, connected to one another by way of a bus320.

The CPU 301 governs overall control of the monitor position determiningapparatus 300. The ROM 302 stores therein programs such as a bootprogram. The RAM 303 is used as a work area of the CPU 301. The magneticdisk drive 304, under the control of the CPU 301, controls thereading/writing of data from/to the magnetic disk 305. The magnetic disk305 stores therein the data written under control of the magnetic diskdrive 304.

The optical disk drive 306, under the control of the CPU 301, controlsreading/writing of data from/to the optical disk 307. The optical disk307 stores therein the data written under control of the optical diskdrive 306, the data being read by a computer.

The display 308 displays, for example, data such as text, images,functional information, etc., in addition to a cursor, icons, and/ortool boxes. A cathode ray tube (CRT), a thin-film-transistor (TFT)liquid crystal display, a plasma display, etc., may be employed as thedisplay 308.

The I/F 309 is connected to a network 314 such as a local area network(LAN), a wide area network (WAN), and the Internet through acommunication line and is connected to other apparatuses through thenetwork 314. The I/F 309 administers an internal interface with thenetwork 314 and controls the input/output of data from/to externalapparatuses. For example, a modem or a LAN adaptor may be employed asthe I/F 309.

The keyboard 310 includes, for example, keys for inputting letters,numerals, and various instructions and performs the input of data.Alternatively, a touch-panel-type input pad or numeric keypad, etc. maybe adopted. The mouse 311 performs the movement of the cursor, selectionof a region, or movement and size change of windows. A track ball or ajoy stick may be adopted provided each respectively has a functionsimilar to a pointing device.

The scanner 312 optically reads an image and takes in the image datainto the monitor position determining apparatus 300. The scanner 312 mayhave an optical character recognition (OCR) function as well. Theprinter 313 prints image data and text data. The printer 313 may be, forexample, a laser printer or an ink jet printer.

FIG. 4 is a schematic of contents recorded in a parameter/yieldsensitivity table. As depicted in FIG. 4, a parameter/yield sensitivitytable 400 stores circuit element information entries 400-1 to 400-nconcerning the circuit elements arranged in a layout of thesemiconductor device.

Specifically, for each circuit element, a corresponding circuit elementinformation entry 400-1 to 400-n includes a circuit element ID, an Xcoordinate, a Y coordinate, a gate length, a gate width, and a yieldsensitivity. The circuit element ID is an identifier that uniquelyidentifies a circuit element. The X coordinate and the Y coordinateindicate an arrangement position of a circuit element in the layout ofthe semiconductor device. The gate length and the gate width are a gatelength and a gate width of a circuit element.

In this example, the circuit element information entries 400-1 to 400-nare sorted in descending order of yield sensitivity of the circuitelements P1 to Pn. That is, a magnitude relationship “S1>S2> . . . >Si>. . . >Sn” is obtained with the yield sensitivity S1 of the circuitelement P1 arranged at the top. From the circuit element informationentries 400-1 to 400-n, an arrangement position (Xi, Yi), a gate lengthLi, a gate width Wi, and a yield sensitivity Si for each circuit elementPi can be recognized (i=1, 2, . . . , n).

A function of the parameter/yield sensitivity table 400 is realized bystorage areas, such as the RAM 303, the magnetic disk 305, and theoptical disk 307 depicted in FIG. 3. Although plural semiconductordevices are formed on the semiconductor wafer, it is assumed that all ofthe semiconductor devices are of the same type in this embodiment.

Therefore, the circuit element information entries 400-1 to 400-n arecommon to all the semiconductor devices formed on the semiconductorwafer. When multiple types of semiconductor devices are formed on thesemiconductor wafer, information corresponding to the circuit elementinformation entries 400-1 to 400-n is included for each type ofsemiconductor device.

FIG. 5 is a functional diagram of the monitor position determiningapparatus according to the first embodiment. The monitor positiondetermining apparatus 300 includes an acquiring unit 501, a selectingunit 502, a determining unit 503, a calculating unit 504, an output unit505, and a converting unit 506.

A function of a control unit (the acquiring unit 501 to the convertingunit 506) is realized by, for example, the CPU 301 executing a programstored in a storage area, such as the ROM 302, the RAM 303, the magneticdisk 305, and the optical disk 307 depicted in FIG. 3 or by an I/F 309.

The acquiring unit 501 has a function of acquiring design dataconcerning the circuit elements arranged in the layout of thesemiconductor device and for each circuit element, yield sensitivitydata indicative of a percentage of a change with respect to a yieldratio of the semiconductor device. The semiconductor device means anarbitrary semiconductor device selected from among the semiconductordevices formed on the semiconductor wafer.

The design data is information that specifies a dimension and thearrangement position for each circuit element (e.g., a transistor, awiring line, a resistor, a capacitor, etc.). Specifically, the designdata is information including, e.g., a net list, floor plan information,and layout information of the semiconductor device.

The yield sensitivity data is information indicative of a percentage ofchange with respect to yield ratio (circuit delay, leak fluctuation,etc.) when a gate length, a gate width, etc. of a circuit element haschanged. For each circuit element, yield sensitivity can be obtained by,for example, using a computational expression acquired at a design stageby a statistical analysis technique.

Specifically, for example, the yield sensitivity of a leak fluctuationwith respect to a yield ratio when a gate length of a circuit elementhas changed can be obtained using equation (1), where n is the totalnumber of circuit elements in the semiconductor device; Si is a yieldsensitivity of the circuit element Pi (i=1, 2, . . . , n); IS(i)(L1, L2,. . . , Li, . . . , Ln) is an equation for calculating the yieldsensitivity for the circuit element Pi; Li is a gate length of thecircuit element Pi; and I_(x)(L1, L2, . . . , Li, . . . , Ln) is a leakvalue function of a yield ratio x (0≦x≦1).

$\begin{matrix}\begin{matrix}{{Si} = {{{IS}(i)}( {{L\; 1},{L\; 2},\ldots\mspace{20mu},{Li},\ldots\mspace{14mu},{Ln}} )}} \\{= {( {{\partial I_{x}}/{\partial{Li}}} )( {{L\; 1},{L\; 2},\ldots\mspace{14mu},{Li},\ldots\mspace{14mu},{Ln}} )}}\end{matrix} & (1)\end{matrix}$

The equation for calculating yield sensitivity (a leak value function)can be obtained by using, for example, a statistical analysis techniqueat the design stage. A specific technique for obtaining the equation tocalculate yield sensitivity (the leak value function) is a knowntechnology and although an explanation thereof will be omitted herein,reference can be made to, for example, Agarwal, Aseem, “CircuitOptimization using Statistical Static Timing Analysis”, Proc. DAC2005,pp. 321-324; and Mani, Murari, “An Efficient Algorithm for StatisticalMinimization of Total Power under Timing Yield Constrains”, Proc.DAC2005, pp. 309-314.

The design data and the yield sensitivity data acquired by the acquiringunit 501 are sorted, for example, in descending order of yieldsensitivity of the circuit elements, and are stored in theparameter/yield sensitivity table 400 depicted in FIG. 4. The designdata and the yield sensitivity data may be input through a usermanipulation of the keyboard 310 or the mouse 311 depicted in FIG. 3, ormay be acquired based on extraction from a database or a library.

The selecting unit 502 has a function of selecting an arbitrary circuitelement from the circuit element group arranged in the layout of thesemiconductor device, based on the yield sensitivity data acquired bythe acquiring unit 501. Specifically, for example, the parameter/yieldsensitivity table 400 is referenced to select the circuit element P1having the greatest yield sensitivity among the circuit elements P1 toPn. A selection result is stored in a storage area, such as the RAM 303,the magnetic disk 305, and the optical disk 307.

The determining unit 503 has a function of determining the arrangementposition of the circuit element selected by the selecting unit 502 inthe layout of the semiconductor device to be an installation position ofa monitor that measures a physical amount of the semiconductor device ina measurement region. The arrangement position of each circuit elementin the layout of the semiconductor device can be specified from thedesign data acquired by the acquiring unit 501.

In the example, the determining unit 503 determines the arrangementposition (X1, Y2) of the circuit element P1 specified from theparameter/yield sensitivity table 400 to be an installation position ofa monitor. A determination result is stored in a storage area, such asthe RAM 303, the magnetic disk 305, and the optical disk 307.

The selection processing performed by the selecting unit 502 may berepeatedly executed until, for example, there are no circuit elementsthat have yet to be selected among the circuit element group, or untilthe number of the monitors assigned installation positions determined bythe determining unit 503 reaches a preset number (hereinafter, “monitornumber Kc”).

For example, when the monitor number Kc of the monitors that can beprovided in one semiconductor device on the semiconductor wafer is setto “5”, the selection processing performed by the selecting unit 502 isrepeatedly executed until there are no circuit elements that have yet tobe selected among the circuit element group or until the number ofmonitors having installation positions determined by the determiningunit 503 reaches “5”.

The monitor number Kc is, for example, a numerical value set accordingto each semiconductor device (or each type of semiconductor device)formed on the semiconductor wafer, and can be set arbitrarily by a usermanipulation of the keyboard 310 or the mouse 311 depicted in FIG. 3.The set monitor number Kc is stored in a storage area, such as the RAM303, the magnetic disk 305, and the optical disk 307.

A specific numerical value set as the monitor number Kc is determinedbased on a fabrication lead time until a product is brought to market ora required quality. Specifically, although a physical amount of thesemiconductor device can be measured in a wider range when the monitornumber Kc is increased, the measuring time also increases; hence, anappropriate numerical value according to fabrication lead time orproduct quality is set.

The selecting unit 502 may select a circuit element having the greatestyield sensitivity among circuit elements that have yet to be selectedamong the circuit element group. Specifically, for example, theparameter/yield sensitivity table 400 is referenced to select thecircuit elements P1 to Pn in descending order of the yield sensitivitiesS1 to Sn (the circuit element P1→the circuit element P2→ . . . ).

Here, an installation position for each monitor is determined withconsideration of the degree of similarity between variations of thecircuit elements to prevent regions in the semiconductor device havingsimilar variations concerning the layout (variations of a process) frombeing redundantly measured. Specifically, for example, variations of thecircuit elements whose arrangement positions in the layout are close toeach other are similar, and variations of the circuit elements whosegate lengths or gate widths are substantially equivalent are similar. Itcan be said that variations are similar when a correlation of variationdistributions is large, and that variations differ when a correlation ofvariation distributions is small.

The calculating unit 504 has a function of calculating the degree ofsimilarity between variations of a circuit element selected by theselecting unit 502 (hereinafter, “selected element”) and a circuitelement determined as a monitor installation position by the determiningunit 503 (hereinafter, “monitor element”), based on the design dataacquired by the acquiring unit 501. Here, when plural monitor elementsare present, the degree of similarity between variations of therespective monitor elements and a selected element is calculated. Anobtained calculation result is stored in a storage area, such as the RAM303, the magnetic disk 305, and the optical disk 307.

Specifically, for example, the calculating unit 504 may calculate adistance between a vector obtained by arranging design data concerning aselected element in the vector space and a vector obtained by arrangingdesign data concerning the monitor element in the vector space. That is,a distance between vectors obtained by arranging various kinds ofparameters that are variation factors is calculated as an index that isused to judge a degree of similarity between circuit elements. Thedegree of similarity between circuit elements decreases as the distanceincreases, and the degree of similarity between circuit elementsincreases as the distance decreases.

Assuming that parameters that are variation factors include an Xcoordinate and a Y coordinate of an arrangement position, a gate length,and a gate width of each of the circuit elements P1 to Pn, then adistance R_(ji) between a vector of a selected element Pi and a vectorof a monitor element Pj can be obtained by using, for example, equation(2), where i=1, 2, . . . , n, j=1, 2, . . . , n (j≠i); a_(X), a_(Y),a_(L), and a_(W) are parameter (the X coordinate, the Y coordinate, thegate length, and the gate width) specific distance coefficients.R _(ji) =a _(x)(Xj−Xi)² +aY(Yj−Yi)2+aL(Lj−Li)2+aW(Wj−Wi)2  (2)

The distance coefficients a_(X), a_(Y), a_(L), and a_(W) in equation (2)can be arbitrarily set. Equation (2) may be input by, for example, auser manipulation of the keyboard 310 or the mouse 311, or may beacquired based on extraction from a database or a library. The inputequation (2) is stored in a storage area, such as the RAM 303, themagnetic disk 305, and the optical disk 307.

The determining unit 503 determines the arrangement position of theselected element to be an installation position of the monitor based ona calculation result obtained by the calculating unit 504. Specifically,for example, the determining unit 503 may determine the arrangementposition of the selected element to be an installation position of amonitor when a distance between vectors calculated by the calculatingunit 504 is larger than a preset threshold value. An obtaineddetermination result is stored in a storage area, such as the RAM 303,the magnetic disk 305, and the optical disk 307.

The threshold value is arbitrarily set with respect to each circuitelement (each selected element) in the semiconductor device in advance.In this example, it can be said that variations of the selected elementand the monitor element are similar when a distance between vectorscalculated by the calculating unit 504 is not greater than the thresholdvalue of the selected element. A distance between vectors calculated bythe calculating unit 504 will be referred to as a “vector distance”, anda threshold value concerning the distance and set with respect to eachcircuit element will be referred to as a “similar-vector-distance”hereinafter.

FIG. 6 is a schematic of contents recorded in a similar-vector-distancetable. As depicted in FIG. 6, a similar-vector-distance table 600 storessimilar-vector-distances R1 to Rn for the respective circuit elements P1to Pn.

From the similar-vector-distance table 600, the similar-vector-distancesR1 to Rn of the respective circuit elements P1 to Pn can be recognized.The similar-vector-distance table 600 may be input by a usermanipulation of the keyboard 310 or the mouse 311 depicted in FIG. 3, ormay be acquired based on extraction from a database or a library. Theinput similar-vector-distance table 600 is stored in a storage area,such as the RAM 303, the magnetic disk 305, and the optical disk 307.

Assuming that the selected element is the circuit element P3 and themonitor element is the circuit element P1 among the circuit elements P1to Pn, the calculating unit 504 refers to the parameter/yieldsensitivity table 400 and substitutes values for various parameters intoequation (2) to obtain a vector distance R₁₃ between the circuit elementP1 and the circuit element P3.

Thereafter, the determining unit 503 refers to thesimilar-vector-distance table 600 and compares the vector distance R₁₃(the distance between the circuit element P1 and the circuit element P3)with a similar-vector-distance R3 of the circuit element P3 (theselected element). If “R₁₃>R3”, the arrangement position of the circuitelement P3 is determined as an installation position a monitor.

When plural monitor elements are present, respective vector distancesbetween the monitor elements and the selected element are calculated.The number of the monitor elements will be referred to as “Z”hereinafter. For example, when the monitor elements include not only thecircuit element P1 but also the circuit element P2 (Z=2) the calculatingunit 504 uses equation (2) to obtain the vector distance R₁₃ between thecircuit element P1 and the circuit element P3 and a vector distance R₂₃between the circuit element P2 and the circuit element P3.

The determining unit 503 compares the vector distance R₁₃ with thesimilar-vector-distance R3 and also compares the vector distance R₂₃with the similar-vector-distance R3. The arrangement position of thecircuit element P3 is determined to be an installation position of amonitor only when “R₁₃>R3” and “R₂₃>R3” are true.

When the monitor elements are present in this manner, vector distancesbetween the monitor elements and the selected element are calculated andcompared with the similar-vector-distance of the selected element. Thearrangement position of the selected element is determined to be aninstallation position of a monitor only when all the vector distancesare larger than the similar-vector-distance.

The output unit 505 has a function of outputting installation positionsof the monitors determined by the determining unit 503. Specifically,for example, the output unit 504 may output monitor position informationindicative of installation positions of the monitors in the layout ofthe semiconductor device. Forms of output by the output unit 505include, for example, display on the display 308, print output by theprinter 313, and transmission to an external device by the I/F 309. Theoutput from the output unit may be stored in a storage area, such as theRAM 303, the magnetic disk 305, and the optical disk 307.

FIG. 7 is a schematic of an exemplary monitor position table. Asdepicted in FIG. 7, a monitor position table 700 includes monitorposition information entries 700-1 to 700-m indicative of installationpositions of monitors M1 to Mm in the layout of the semiconductordevice.

Specifically, the monitor position information entries 700-1 to 700-mrespectively include a monitor ID, an X coordinate, and a Y coordinate.The monitor ID is an identifier that uniquely identifies a monitor. TheX coordinate and the Y coordinate are indicative of a coordinateposition in a coordinate system of the semiconductor device. From themonitor position table 700, coordinate positions of the monitor M1 to Mmin the coordinate system of the semiconductor device can be recognized.For example, a coordinate position of a monitor Mk is(X,Y)=(X_(c)k,Y_(c)k).

Plural semiconductor devices (chips) are formed on the semiconductorwafer. For example, when a wafer size (a diameter) of the semiconductorwafer is “300 mm” and a chip size thereof is “7×7 mm”, approximately1360 semiconductor devices are formed on the semiconductor wafer.However, installation positions of the monitors determined by theabove-explained technique are coordinate positions in the coordinatesystem of each semiconductor device.

Therefore, the installation positions of the monitors in the coordinatesystem of the semiconductor device must be converted into coordinates tospecify the installation positions of the monitors in a coordinatesystem of the semiconductor wafer when the APC is applied. A specifictechnique for converting the installation positions of the monitors intocoordinates will be explained hereinafter. An example where psemiconductor devices C1 to Cp that are of the same type and are formedon the semiconductor wafer will be explained.

An original point table storing original point positions of thesemiconductor devices C1 to Cp on the semiconductor wafer will beexplained first. FIG. 8 is a schematic of an exemplary original pointtable. As depicted in FIG. 8, an original point table 800 stores Xcoordinates and Y coordinates indicative of original point positions ofthe semiconductor devices C1 to Cp formed on the semiconductor wafer.The X coordinates and the Y coordinates here are those in the coordinatesystem of the semiconductor wafer.

From the original point table 800, original point positions of thesemiconductor devices C1 to Cp in the coordinate system of thesemiconductor wafer can be specified. For example, an original pointposition of a semiconductor device Cr is (X,Y)=(X_(o)r,Y_(o)r). Theoriginal point table 800 may be input by, for example, a usermanipulation of the keyboard 310 or the mouse 311, or may be acquiredbased on extraction from a database or a library. The input originalpoint table 800 is stored in a storage area, such as the RAM 303, themagnetic disk 305, and the optical disk 307.

The explanation with reference to FIG. 5 continues. The converting unit506 has a function of using an original point position of thesemiconductor device on the semiconductor wafer and an arrangementposition determined as an installation position of the monitor by thedetermining unit 503 to convert the installation position of the monitorin the coordinate system of the semiconductor device into aninstallation position of the monitor in the coordinate system of thesemiconductor wafer. An obtained conversion result is stored in astorage area, such as the RAM 303, the magnetic disk 305, and theoptical disk 307.

Specifically, for example, an installation position of the monitor inthe coordinate system of the semiconductor device can be converted intoan installation position of the monitor in the coordinate system of thesemiconductor wafer using equations (3) and (4), where an X coordinateof a monitor M_(w)q in the coordinate system of the semiconductor waferis X_(w)q; a Y coordinate of the same is Y_(w)q; the total number of themonitors on the semiconductor wafer is mp; q=1, 2, . . . , mp; r=1, 2, .. . , p; and i=1, 2, . . . , n.X _(w) q=X _(o) r+Xi  (3)Y _(w) q=Y _(o) r+Yi  (4)

For example, if a coordinate position (X_(o) 1,Y_(o) 1) of a monitor M1in the coordinate system of the semiconductor device C1 is convertedinto a coordinate position in the coordinate system of the semiconductorwafer, since r=1, i=1, and q=1×1=1, then, (X_(w) 1,Y_(w) 1)=(X_(o)1+X1,Y_(o) 1+Y1).

Equations (3) and (4) may be input by, for example, a user manipulationof the keyboard 310 or the mouse 311, or may be acquired based onextraction from a database or a library. The input equations (3) and (4)are stored in a storage area, such as the RAM 303, the magnetic disk305, and the optical disk 307.

The output unit 505 may output a converted installation position of themonitor obtained by the converting unit 506. A specific example of anoutput result obtained by the output unit 505 will be explained. FIG. 9is schematic of another exemplary monitor position table. As depicted inFIG. 9, a monitor position table 900 includes monitor positioninformation entries 900-1 to 900-mp indicative of installation positionsof monitors M_(w) 1 to M_(w)mp on the semiconductor wafer.

Specifically, the monitor position information entries 900-1 to 900-mprespectively include a monitor ID, an X coordinate, and a Y coordinate.From the monitor position table 900, coordinate positions of themonitors M1 to Mmp in the coordinate system of the semiconductor wafercan be recognized. For example, a coordinate position of the monitorM_(w)q in the coordinate system of the semiconductor wafer is(X,Y)=(X_(w)q,Y_(w)q).

Among the monitors M_(w) 1 to M_(w)mp to be mounted on the semiconductorwafer, the converting unit 506 may perform coordinate conversion withrespect to only a monitor to be mounted at a position critical in termsof process of the semiconductor wafer (e.g., an edge of thesemiconductor wafer). Specifically, for example, information thatspecifies an edge of a semiconductor wafer and an original pointposition of a semiconductor device on the semiconductor wafer are usedto specify a semiconductor device formed at the edge of thesemiconductor wafer.

A monitor that is to be provided at an arrangement position of thesemiconductor device is specified, and this monitor alone is subject tocoordinate conversion from the coordinate system of the semiconductordevice to the coordinate system of the semiconductor wafer. The edge ofthe semiconductor wafer represents, for example, a region on an innerside, approximately three to five percent of a diameter from an end ofthe semiconductor wafer. The information that specifies the edge of thesemiconductor wafer may be preset, or may be input by a usermanipulation of the keyboard 310 or the mouse 311. Thus, a coordinateposition of the monitor that measures a physical amount at a positioncritical in terms of process and circuit in the coordinate system of thesemiconductor wafer can be recognized.

FIGS. 10 and 11 are flowcharts of an example of processing fordetermining monitor position.

As depicted in the flowchart of FIG. 10, it is determined whether theacquiring unit 501 has acquired design data concerning each circuitelement arranged in the layout of the semiconductor device formed on thesemiconductor wafer and for each circuit element, yield sensitivity dataindicative of a percentage of a change with respect to a yield ratio ofthe semiconductor device (step S1001).

Waiting occurs for the design data and the yield sensitivity data to beacquired (step S1001: NO); if the data are acquired (step S1001: YES),the design data and the yield sensitivity data are sorted in descendingorder of yield sensitivity (step S1002) and stored in theparameter/yield sensitivity table 400 (step S1003).

The selecting unit 502 refers to the parameter/yield sensitivity table400 to select the element P1 having the greatest yield sensitivity amongthe circuit elements P1 to Pn (step S1004), and the determining unit 503determines the arrangement position of the selected element P1 in thelayout of the semiconductor device to be an installation position of amonitor that measures a physical amount on the semiconductor device in ameasurement region (step S1005).

Subsequently, i=1 and Z=1 are set (step S1006), and whether “i≧n” or“Z≧Kc” is true is judged (step S1007). When “i<n” or “Z<Kc” is true(step S1007: NO), the processing advances to step S1010 depicted in FIG.11. Z represents the number of the monitor elements and Kc representsthe number of the monitors that can be provided in the semiconductordevice.

When “i≧n” or “Z≧Kc” is true (step S1007: YES), the converting unit 506uses an original point position of the semiconductor device on thesemiconductor wafer and the arrangement position of the monitor elementdetermined as the installation position of the monitor by thedetermining unit 503 to convert the installation position of the monitorin the coordinate system of the semiconductor device into aninstallation position of the monitor in the coordinate system of thesemiconductor wafer (step S1008).

The output unit 505 outputs the monitor position table 900 storing theinstallation position of the monitor converted by the converting unit506 (step S1009), and a series of processing based on the flowchart isterminated.

Subsequently, in the flowchart depicted in FIG. 11, the selecting unit502 refers to the parameter/yield sensitivity table 400 to select anelement PI (where I=i+1) from the circuit elements P1 to Pn (stepS1010).

The calculating unit 504 calculates a vector distance R_(JI) between theselected element PI and a monitor element PJ (where PJ is a circuitelement ID set of monitor elements) using equation (2) (step S1011).Here, in equation (2), “i→I” and “j→J”.

Thereafter, the determining unit 503 determines whether “R_(JI)>RI” istrue (step S1012). If “R_(JI)>RI” is true (step S1012: YES), thearrangement position of the selected element PI is determined to be aninstallation position of a monitor (step S1013). Z is incremented by one(step S1014), i is also incremented by one (step S1015), and theprocessing advances to step S1007 depicted in FIG. 10.

If “R_(JI)≦RI” is true at the step S1012 (step S1012: NO) is incrementedby one (step S1015), and the processing proceeds to step S1007 depictedin FIG. 10.

According to the first embodiment explained above, an arrangementposition of a circuit element that is critical to a yield ratio ofcircuit delay or a leak fluctuation can be determined as an installationposition of a monitor by using the yield sensitivity of each circuitelement in the semiconductor device. Similarities between variations ofcircuit elements can be calculated using a value of each parameter thatis a variation factor concerning the layout.

The arrangement position of a circuit element having a differentvariation can be determined as an installation position of a monitorwhile considering the degree of similarity between variations of thecircuit elements. As a result, multiple variations in the semiconductordevice can be controlled with the limited number of monitors. Performingcoordinate conversion of an installation position of a monitor in thecoordinate system of the semiconductor device enables specification ofan installation position of the monitor in the coordinate system of thesemiconductor wafer.

Thus, according to the first embodiment, a physical amount of thesemiconductor device can be efficiently and effectively measured with alimited number of monitors, and controlling circuit dependent variationsat a design stage based on a result of this measurement enables improvedfabrication yield of the semiconductor device.

In the first embodiment, the technique of determining, as aninstallation position of a monitor, the arrangement position of eachcircuit element whose variation is not similar to that of a monitorelement determined as the installation position of the monitor, thedetermination being made in descending order of yield sensitivity amongthe circuit element group in the semiconductor device, is explained.

In a second embodiment, a technique of first narrowing down a set ofcircuit elements each having a yield sensitivity equal to or above apredetermined threshold value from a circuit element group as a set ofmonitor element candidates and then determining, as an installationposition of a monitor, the arrangement position of each circuit elementwhose variation is not similar to that of a monitor element determinedas the installation position of a monitor as far as possible indescending order of yield sensitivity from the narrowed candidate setwill be explained. Diagrammatic representations and explanations ofparts equivalent to those explained in the first embodiment will beomitted.

FIG. 12 is a schematic of an overview of a monitor position determiningtechnique according to the second embodiment. As depicted in FIG. 12,vectors V1 to V4 of circuit elements P1 to P4 are depicted as axes in avector space 1200 having three parameters (an X coordinate, a Ycoordinate, and a gate length) that are variation factors. These circuitelements P1 to P4 form a set of candidates each having a yieldsensitivity equal to or above a predetermined threshold value.

In this example, each of the circuit elements P1 and P2 is a monitorelement already determined as a monitor installation position. In thiscase, vector distances between circuit elements P3 and P4 (undeterminedelements) that are not determined as monitor installation positionsamong the set of candidates P1 to P4 and the monitor elements P1 and P2are obtained. Specifically, vector distances {R₁₃, R₂₃} between theundermined element P3 and the monitor elements P1 and P2 and vectordistances {R₁₄, R₂₄} between the undetermined element P4 and the monitorelements P1 and P2 are obtained.

The smallest vector distance (e.g., the vector distance R₁₃) that is thesmallest among the vector distances {R₁₃, R₂₃} is compared with thesmallest vector distance (e.g., the vector distance R₂₄) that is thesmallest among the vector distances {R₁₄, R₂₄} to identify the largestamong the smallest vector distances compared (e.g., the vector distanceR₂₄).

The arrangement position of the circuit element associated with theidentified largest vector distance is determined as an installationposition of a monitor. For example, when the vector distance R₂₄ isselected as the largest vector distance, the arrangement position of thecircuit element P4 associated therewith can be determined to be aninstallation position of a monitor.

As explained above, according to the second embodiment, the arrangementposition of the circuit element P4, which is apart from (whose variationis not similar to those of) the monitor elements P1 and P2 alreadydetermined as installation positions of monitors, is determined as aninstallation position of a monitor in descending order of yieldsensitivity from among the set of the candidates P1 to P4 narrowed downfrom the circuit element group. As a result, more variations can becovered.

FIG. 13 is a functional diagram of a monitor position determiningapparatus according to the second embodiment. A monitor positiondetermining apparatus 1300 includes the acquiring unit 501, theselecting unit 502, the determining unit 503, the calculating unit 504,the output unit 505, the converting unit 506, and a detecting unit 1301.A function of a control unit (the acquiring unit 501 to the convertingunit 506, and the detecting unit 1301) is realized by the CPU 301executing a program stored in a storage area, such as the ROM 302, theRAM 303, the magnetic disk 305, and the optical disk 307 depicted inFIG. 3 or by using the I/F 309.

The detecting unit 1301 has a function of detecting, based on yieldsensitivity data acquired by the acquiring unit 501 and from among acircuit element group arranged in a layout of a semiconductor device, aset of circuit elements (a set of candidates for monitor elements) eachhaving a yield sensitivity equal to or above a preset threshold value.Specifically, for example, the parameter/yield sensitivity table 400depicted in FIG. 4 is referenced to detect a set of candidates eachhaving a yield sensitivity equal to or above a preset threshold valueSc.

The threshold value Sc may be input by a user manipulation of thekeyboard 310 or the mouse 311 depicted in FIG. 3 or may be acquiredbased on extraction from a database or a library. The input thresholdvalue Sc and an obtained detection result are stored in a storage area,such as the RAM 303, the magnetic disk 305, and the optical disk 307.

The selecting unit 502 selects an arbitrary circuit element from thecandidate set detected by the detecting unit 1301. Specifically, forexample, a circuit element having the highest yield sensitivity may beselected from the candidate set. The determining unit 503 thendetermines the arrangement position of the circuit element selected bythe selecting unit 502 to be an installation position of a monitor.

The selecting unit 502 further selects, from the candidate set, anunselected circuit element that has not been determined as aninstallation position of a monitor. The calculating unit 504 calculates,based on design data acquired by the acquiring unit 501, a degree ofsimilarity between fabrication variations of the undetermined circuitelement that is selected by the selecting unit 502 and has not beendetermined to be an installation position of a monitor and the circuitelement that has been determined to be an installation position of amonitor by the determining unit 503.

Specifically, for example, a distance between a vector obtained byarranging design data concerning an undetermined circuit element(hereinafter, “undetermined element”) that has not been determined as aninstallation position of a monitor in a vector space and a vectorobtained by arranging design data concerning a circuit element that hasbeen determined as an installation position of a monitor (a monitorelement) in the vector space may be calculated.

More specifically, for example, a distance d(α,β) between a vector of anundetermined element Pα and a vector of a monitor element Pβ can beobtained using equation (5), where α is a circuit element number of theundetermined element (a number part of a circuit element ID) and β is acircuit element number of the monitor element. It is assumed thatparameters that are variation factors include an X coordinate and a Ycoordinate of an arrangement position, a gate length, and a gate widthof each of the circuit elements P1 to Pn.

It is further assumed that a set of candidates each having a yieldsensitivity equal to or above the preset threshold value Sc includes thecircuit elements P1 to PN among the circuit elements P1 to Pn, and a setof circuit element numbers of these circuit elements is IC (IC=1, 2, . .. , N). A set of circuit element numbers of monitor elements is IM. Arelationship of αεIC and βεIM is achieved with respect to each circuitelement number.d(α,β)=a _(X)(Xα−Xβ)2+a _(Y)(Yα−Yβ)2+a _(L)(Lα−Lβ)2+a _(W)(Wα−Wβ)2  (5)

The determining unit 503 determines the installation position of eachmonitor based on a calculation result obtained by the calculating unit504. Specifically, for example, the arrangement position of a circuitelement having the largest inter-vector distance calculated by thecalculating unit 504 and among the undetermined circuit elements thathave not been determined as installation positions of monitors may bedetermined to be an installation position of a monitor.

More specifically, for example, using equation (6) where d(α) is thelargest distance between a vector of the undetermined element Pα and avector of the monitor element Pβ, a circuit element having the largestinter-vector distance can be specified from among undetermined circuitelements that have not been determined to be installation positions ofmonitors.d(α)=minβε_(IM) d(α,β)  (6)

The determining unit 503 determines, as an installation position of amonitor, the arrangement position of the undetermined element Pαassociated with d(α) obtained using equation (6). Equations (5) and (6)may be input by a user manipulation of, e.g., the keyboard 310 or themouse 311, or may be acquired based on extraction from a database or alibrary. The input equations (5) and (6) are stored in a storage area,such as the RAM 303, the magnetic disk 305, and the optical disk 307.

FIGS. 14 and 15 are flowcharts of an example of processing by themonitor position determining apparatus 1300 to determine monitorposition.

As depicted in the flowchart of FIG. 14, it is determined whether theacquiring unit 501 has acquired design data concerning each circuitelement arranged in the layout of the semiconductor device formed on thesemiconductor wafer and for each circuit element, yield sensitivity dataindicative of a percentage of a change with respect to a yield ratio ofthe semiconductor device (step S1401).

Waiting occurs for the design data and the yield sensitivity data to beacquired (step S1401: NO); if the data are acquired (step S1401: YES),the design data and the yield sensitivity data are sorted in descendingorder of yield sensitivity (step S1402) and stored in theparameter/yield sensitivity table 400 (step S1403).

The detecting unit 1301 refers to the parameter/yield sensitivity table400 to detect a set of monitor element candidates each having a yieldsensitivity equal to or above the preset threshold value Sc from amongthe circuit elements P1 to Pn (step S1404). The selecting unit 502refers to the parameter/yield sensitivity table 400 to select thecircuit element P1 having the greatest yield sensitivity among thecandidate set (step S1405).

Subsequently, the determining unit 503 determines the arrangementposition of the circuit element P1 to be an installation position of amonitor (step S1406), sets the number of monitor elements Z to Z=1,deletes a circuit element number 1 of the circuit element P1 from thecircuit element number set IC of the candidate set, and registers thecircuit element number 1 in the circuit element number set IM of themonitor elements (step S1407), and the processing advances to step S1408depicted in FIG. 15.

As depicted in the flowchart of FIG. 15, it is determined whether “Z≧Kc”is true (step S1408). If “Z<Kc” is true (step S1408: NO), the selectingunit 502 selects, from the candidate set, an arbitrary undeterminedelement Pα that has not been determined to be an installation positionof a monitor (step S1409).

The calculating unit 504 calculates a vector distance d(α,β) between theundetermined element Pα and the monitor element Pβ (step S1410). Kc isthe number of monitors that can be provided in the semiconductor device.It is determined whether an undetermined element Pα that has yet to beselected from the candidate set is present (step S1411). If anundetermined element Pα that has yet to be selected is present (stepS1411: YES), the processing returns to step S1409.

If an undetermined element Pα that has yet to be selected is not present(step S1411: NO), the determining unit 503 specifies the undeterminedelement Pα having the largest vector distance d(α,β) calculated at thestep S1410 (step S1412) and determines the arrangement position of thespecified undetermined element Pα to be an installation position of amonitor (step S1413).

Then, a circuit element number α of the undetermined element Pα isdeleted from the circuit element number set IC of the candidate set, thecircuit element number α is added to the circuit element number set IMof the monitor elements (step S1414), the number of monitor elements Zis incremented by one (step S1415), and the processing returns to stepS1408.

If “Z≧Kc” is true at the step S1408 (step S1408: YES), the convertingunit 506 uses an original point position of the semiconductor device onthe semiconductor wafer and the arrangement position of the monitorelement determined as an installation position of a monitor by thedetermining unit 503 to convert the installation position of the monitorin the coordinate system of the semiconductor device into aninstallation position of the monitor in the coordinate system of thesemiconductor wafer (step S1416).

Lastly, the output unit 505 outputs monitor position informationindicative of the converted installation position of the monitorobtained by the converting unit 506 (step S1417), thereby terminating aseries of processing based on this flowchart.

According to the second embodiment explained above, the monitor elementcandidate set can be arbitrarily narrowed down by providing thethreshold value Sc concerning the yield sensitivities. For example, whenthe threshold value Sc concerning the yield sensitivities is set to alow value, the processing time tends to increase as the number ofcircuit elements included in the candidate set increases; however,product quality can be improved. On the other hand, when the thresholdvalue Sc is set to a high value, the processing time can be reducedwhile maintaining the product quality to some extent.

The arrangement position of a circuit element, having the largest vectordistance from a monitor element (a circuit element already determined tobe an installation position of a monitor) and among undeterminedelements included in the candidate set, can be determined to be aninstallation position of a monitor. As a result, the installationpositions of the monitors can be appropriately dispersed to thearrangement positions of circuit elements having different variations,enabling control of more variations.

The monitor position determining method explained in the presentembodiments can be implemented by a computer, such as a personalcomputer and a workstation, executing a program that is prepared inadvance. The program is recorded on a computer-readable recording mediumsuch as a hard disk, a flexible disk, a CD-ROM, an MO, and a DVD, and isexecuted by being read out from the recording medium by a computer. Theprogram can be a transmission medium that can be distributed through anetwork such as the Internet.

The monitor position determining apparatuses 300, 1300 described in thepresent embodiments can be realized by an application specificintegrated circuit (ASIC) such as a standard cell or a structured ASIC,or a programmable logic device (PLD) such as a field-programmable gatearray (FPGA). Specifically, for example, functions of the monitorposition determining apparatuses 300, 1300 (the acquiring unit 501 tothe converting unit 506, the detecting unit 1301) are defined inhardware description language (HDL) which is logically synthesized andapplied to the ASIC, the PLD, etc., thereby enabling fabrication of themonitor position determining apparatuses 300, 1300.

All examples and conditional language recited herein are intended forpedagogical purposes to aid the reader in understanding the inventionand the concepts contributed by the inventor to furthering the art, andare to be construed as being without limitation to such specificallyrecited examples and conditions, nor does the organization of suchexamples in the specification relate to a showing of the superiority andinferiority of the invention. Although the embodiment(s) of the presentinventions have been described in detail, it should be understood thatthe various changes, substitutions, and alterations could be made heretowithout departing from the spirit and scope of the invention.

1. A monitor position determining apparatus comprising: an acquiringunit that acquires design data concerning circuit elements arranged in alayout of a semiconductor device and for each of the circuit elements,yield sensitivity data indicative of a percentage of change with respectto a yield ratio of the semiconductor device; a selecting unit thatselects, based on the yield sensitivity data acquired by the acquiringunit, a circuit element from a circuit element group arranged in thelayout; a determining unit that determines an arrangement position inthe layout to be an installation position of a monitor that measures aphysical amount in the semiconductor device in a measurement region, thearrangement position being of the circuit element that is specified fromthe design data acquired by the acquiring unit and selected by theselecting unit; and an output unit that outputs the installationposition determined by the determining unit.
 2. The monitor positiondetermining apparatus according to claim 1, wherein the selecting unitselects from the circuit element group, a circuit element having agreatest yield sensitivity that is a percentage of change with respectto a yield ratio of the semiconductor device.
 3. The monitor positiondetermining apparatus according to claim 2, further comprising acalculating unit that calculates a degree of similarity betweenvariations of the circuit elements, the variations being related to afabrication process, wherein the selecting unit selects a circuitelement having the greatest yield sensitivity among circuit elementsthat have yet to be selected from the circuit element group, thecalculating unit calculates, based on the design data, a degree ofsimilarity between the variations of the circuit element selected by theselecting unit and a circuit element whose arrangement position has beendetermined to be an installation position of a monitor by thedetermining unit, and the determining unit determines, based on acalculation result obtained by the calculating unit, the arrangementposition of the circuit element selected by the selecting unit to be aninstallation position of a monitor.
 4. The monitor position determiningapparatus according to claim 3, wherein the calculating unit calculatesa distance between a first vector obtained by arranging, in a vectorspace, design data concerning the circuit element selected by theselecting unit and a second vector obtained by arranging, in the vectorspace, design data concerning the circuit element whose arrangementposition has been determined to be an installation position of a monitorby the determining unit, and the determining unit determines thearrangement position of the circuit element selected by the selectingunit to be an installation position of a monitor when the distancebetween the first and the second vectors calculated by the calculatingunit is equal to or greater than a given value.
 5. The monitor positiondetermining apparatus according to claim 3, wherein the yieldsensitivity data is yield sensitivity data with respect to at least oneof a circuit delay and a leak fluctuation of a semiconductor device. 6.The monitor position determining apparatus according to claim 1, furthercomprising a detecting unit that detects, based on the yield sensitivitydata acquired by the acquiring unit and from among the circuit elementgroup, a set of circuit elements each having a yield sensitivity equalto or greater than a given value, wherein the selecting unit selects acircuit element from the circuit element set detected by the detectingunit.
 7. The monitor position determining apparatus according to claim6, wherein the selecting unit selects a circuit element having agreatest yield sensitivity among the circuit element set.
 8. The monitorposition determining apparatus according to claim 7, further comprisinga calculating unit that calculates a degree of similarity betweenvariations of a circuit element whose arrangement position is notdetermined to be an installation position of a monitor and a circuitelement whose arrangement position has been determined to be aninstallation position of a monitor by the determining unit, thevariations being related to a fabrication process, wherein the selectingunit selects from the circuit element set detected by the detectingunit, the circuit element whose arrangement position is not determinedto be an installation position of a monitor, the calculating unitcalculates, based on the design data acquired by the acquiring unit, adegree of similarity between the variations of the circuit element thatis selected by the selecting unit and whose arrangement position is notdetermined to be an installation position of a monitor and the circuitelement whose arrangement position has been determined to be aninstallation position of a monitor, and the determining unit determinesan installation position of a monitor based on a calculation resultobtained by the calculating unit.
 9. The monitor position determiningapparatus according to claim 8, wherein the calculating unit calculatesa distance between a vector obtained by arranging, in a vector space,design data concerning the circuit element whose arrangement position isnot determined to be an installation position of a monitor and a vectorobtained by arranging, in the vector space, design data concerning thecircuit element whose arrangement position has been determined to be aninstallation position of a monitor by the determining unit, and thedetermining unit determines, to be an installation position of amonitor, an arrangement position of a circuit element having a largestinter-vector distance calculated by the calculating unit among thecircuit elements that are not determined to be installation positions ofmonitors.
 10. The monitor position determining apparatus according toclaim 1, further comprising a converting unit that uses an originalpoint position of the semiconductor device on a semiconductor wafer andthe arrangement position determined to be an installation position of amonitor by the determining unit to convert the installation position ofthe monitor in a coordinate system of the semiconductor device into aninstallation position of the monitor in a coordinate system of thesemiconductor wafer, wherein the output unit outputs the convertedinstallation position of the monitor obtained by the converting unit.11. A monitor position determining method comprising: executing by acomputer operations of: acquiring design data concerning circuitelements arranged in a layout of a semiconductor device and for each ofthe circuit elements, yield sensitivity data indicative of a percentageof change with respect to a yield ratio of the semiconductor device;selecting, based on the yield sensitivity data acquired at theacquiring, a circuit element from a circuit element group arranged inthe layout; determining an arrangement position in the layout to be aninstallation position of a monitor that measures a physical amount inthe semiconductor device in a measurement region, the arrangementposition being of the circuit element that is specified from the designdata acquired at the acquiring and selected at the selecting; andoutputting the installation position of the monitor determined at thedetermining.